Accounting for income distribution trends: A density function decomposition approach

This paper develops methods for decomposing changes in the income distribution using subgroup decompositions of the income density function. Overall changes are related to changes in subgroup shares and changes in subgroup densities, where the latter are broken down further using elementary transformations of individual incomes. These density decompositions are analogous to the widely-used decompositions of inequality indices by population subgroup, except that they summarize multiple features of the income distribution (using graphs), rather than focusing on a specific feature such as dispersion, and are not dependent on the choice of a specific summary index. Nonetheless, since inequality and poverty indices can be expressed as PDF functionals, our density-based methods can also be used to provide numerical decompositions of these. An application of the methods reveals the multi-faceted nature of UK income distribution trends during the 1980s.Income distribution ; Inequality ; density functions ; subgroup decomposition

Trends in Individual Income Growth: Measurement Methods and British Evidence

Assessments of whose income growth is the greatest and whose is the smallest are typically based on comparisons of income changes for income groups (e.g. rich versus poor) or income values (e.g. quantiles). However, income group and quantile composition changes over time because of income mobility. To summarize patterns of income growth while also tracking the fortunes of the same individuals, a longitudinal perspective is required. For this case, we develop dominance conditions and summary indices for comparisons of distributions of individual income growth, together with associated methods of estimation and inference. Using these methods and data from the British Household Panel Survey, we study individual income growth for periods between 1991 and 2005. We show that income growth was significantly more pro-poor in the early years of the Labour government than in earlier Conservative years.individual income growth, pro-poor growth, progressive income growth, income mobility, mobility profile, British Household Panel Survey

Trends in income inequality, pro-poor income growth and income mobility

We provide an analytical framework within which changes in income inequality over time are related to the pattern of income growth across the income range, and the reshuffling of individuals in the income pecking order. We use it to explain how it was possible both for ‘the poor’ to have fared badly relatively to ‘the rich’ in the USA during the 1980s (when income inequality grew substantially), and also for income growth to have been pro-poor. Income growth was also pro-poor in Western Germany, more so than in the USA, and inequality did not rise as much.inequality ; income growth ; income mobility ; pro-poor growth ; reranking

A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for the numerical inversion of the Laplace transform is discussed.Comment: 25 pages, 2 figures, Theorem 3.3 has been adde

Dynamics of Income Rank Volatility: Evidence from Germany and the US

This paper presents a methodology for comparing income rank volatility profiles over time and across distributions. While most of the existing measures are affected by changes in marginal distributions, this paper proposes a framework that is based on individuals’ relative positions in the distribution, and is neutral in relation to structural changes that occur in the economy. Applying this approach to investigate rank volatility in Germany and the US over three decades, we show that while poorer individuals within both countries are the most volatile, the volatility trend for the middle class in each of these countries differs